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cantera/src/transport/HighPressureGasTransport.cpp
Ray Speth 4669b9cf5a Fix miscellaneous spelling errors
2016-12-30 13:26:50 -05:00

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/**
* @file HighPressureGasTransport.cpp
* Implementation file for class HighPressureGasTransport
*
* Transport parameters are calculated using corresponding states models:
* Binary diffusion coefficients use the generalized chart described by
* Takahashi, et al. and viscosity calculations use the Lucas method.
* All methods are described in Reid, Prausnitz, and Polling, "The Properties
* of Gases and Liquids, 4th ed., 1987 (viscosity in Ch. 9, Thermal
* conductivity in Ch. 10, and Diffusion coefficients in Ch. 11).
**/
// This file is part of Cantera. See License.txt in the top-level directory or
// at http://www.cantera.org/license.txt for license and copyright information.
#include "cantera/transport/HighPressureGasTransport.h"
#include "cantera/numerics/ctlapack.h"
#include "cantera/base/utilities.h"
#include "cantera/transport/TransportParams.h"
#include "cantera/thermo/IdealGasPhase.h"
#include "cantera/transport/TransportFactory.h"
#include "cantera/base/stringUtils.h"
#include "cantera/transport/MultiTransport.h"
using namespace std;
namespace Cantera
{
HighPressureGasTransport::HighPressureGasTransport(thermo_t* thermo)
: MultiTransport(thermo)
{
}
double HighPressureGasTransport::thermalConductivity()
{
// Method of Ely and Hanley:
update_T();
doublereal Lprime_m = 0.0;
const doublereal c1 = 1./16.04;
size_t nsp = m_thermo->nSpecies();
vector_fp molefracs(nsp);
m_thermo->getMoleFractions(&molefracs[0]);
vector_fp cp_0_R(nsp);
m_thermo->getCp_R_ref(&cp_0_R[0]);
vector_fp L_i(nsp);
vector_fp f_i(nsp);
vector_fp h_i(nsp);
vector_fp V_k(nsp);
m_thermo -> getPartialMolarVolumes(&V_k[0]);
doublereal L_i_min = BigNumber;
for (size_t i = 0; i < m_nsp; i++) {
doublereal Tc_i = Tcrit_i(i);
doublereal Vc_i = Vcrit_i(i);
doublereal T_r = m_thermo->temperature()/Tc_i;
doublereal V_r = V_k[i]/Vc_i;
doublereal T_p = std::min(T_r,2.0);
doublereal V_p = std::max(0.5,std::min(V_r,2.0));
// Calculate variables for density-independent component:
doublereal theta_p = 1.0 + (m_w_ac[i] - 0.011)*(0.56553
- 0.86276*log(T_p) - 0.69852/T_p);
doublereal phi_p = (1.0 + (m_w_ac[i] - 0.011)*(0.38560
- 1.1617*log(T_p)))*0.288/Zcrit_i(i);
doublereal f_fac = Tc_i*theta_p/190.4;
doublereal h_fac = 1000*Vc_i*phi_p/99.2;
doublereal T_0 = m_temp/f_fac;
doublereal mu_0 = 1e-7*(2.90774e6/T_0 - 3.31287e6*pow(T_0,-2./3.)
+ 1.60810e6*pow(T_0,-1./3.) - 4.33190e5 + 7.06248e4*pow(T_0,1./3.)
- 7.11662e3*pow(T_0,2./3.) + 4.32517e2*T_0 - 1.44591e1*pow(T_0,4./3.)
+ 2.03712e-1*pow(T_0,5./3.));
doublereal H = sqrt(f_fac*16.04/m_mw[i])*pow(h_fac,-2./3.);
doublereal mu_i = mu_0*H*m_mw[i]*c1;
L_i[i] = mu_i*1.32*GasConstant*(cp_0_R[i] - 2.5)/m_mw[i];
L_i_min = min(L_i_min,L_i[i]);
// Calculate variables for density-dependent component:
doublereal theta_s = 1 + (m_w_ac[i] - 0.011)*(0.09057 - 0.86276*log(T_p)
+ (0.31664 - 0.46568/T_p)*(V_p - 0.5));
doublereal phi_s = (1 + (m_w_ac[i] - 0.011)*(0.39490*(V_p - 1.02355)
- 0.93281*(V_p - 0.75464)*log(T_p)))*0.288/Zcrit_i(i);
f_i[i] = Tc_i*theta_s/190.4;
h_i[i] = 1000*Vc_i*phi_s/99.2;
}
doublereal h_m = 0;
doublereal f_m = 0;
doublereal mw_m = 0;
for (size_t i = 0; i < m_nsp; i++) {
for (size_t j = 0; j < m_nsp; j++) {
// Density-independent component:
doublereal L_ij = 2*L_i[i]*L_i[j]/(L_i[i] + L_i[j] + Tiny);
Lprime_m += molefracs[i]*molefracs[j]*L_ij;
// Additional variables for density-dependent component:
doublereal f_ij = sqrt(f_i[i]*f_i[j]);
doublereal h_ij = 0.125*pow(pow(h_i[i],1./3.) + pow(h_i[j],1./3.),3.);
doublereal mw_ij_inv = (m_mw[i] + m_mw[j])/(2*m_mw[i]*m_mw[j]);
f_m += molefracs[i]*molefracs[j]*f_ij*h_ij;
h_m += molefracs[i]*molefracs[j]*h_ij;
mw_m += molefracs[i]*molefracs[j]*sqrt(mw_ij_inv*f_ij)*pow(h_ij,-4./3.);
}
}
f_m = f_m/h_m;
mw_m = pow(mw_m,-2.)*f_m*pow(h_m,-8./3.);
doublereal rho_0 = 16.04*h_m/(1000*m_thermo->molarVolume());
doublereal T_0 = m_temp/f_m;
doublereal mu_0 = 1e-7*(2.90774e6/T_0 - 3.31287e6*pow(T_0,-2./3.)
+ 1.60810e6*pow(T_0,-1./3.) - 4.33190e5 + 7.06248e4
*pow(T_0,1./3.) - 7.11662e3*pow(T_0,2./3.) + 4.32517e2*T_0
- 1.44591e1*pow(T_0,4./3.) + 2.03712e-1*pow(T_0,5./3.));
doublereal L_1m = 1944*mu_0;
doublereal L_2m = (-2.5276e-4 + 3.3433e-4*pow(1.12 - log(T_0/1.680e2),2))*rho_0;
doublereal L_3m = exp(-7.19771 + 85.67822/T_0)*(exp((12.47183
- 984.6252*pow(T_0,-1.5))*pow(rho_0,0.1) + (rho_0/0.1617 - 1)
*sqrt(rho_0)*(0.3594685 + 69.79841/T_0 - 872.8833*pow(T_0,-2))) - 1.)*1e-3;
doublereal H_m = sqrt(f_m*16.04/mw_m)*pow(h_m,-2./3.);
doublereal Lstar_m = H_m*(L_1m + L_2m + L_3m);
return Lprime_m + Lstar_m;
}
void HighPressureGasTransport::getThermalDiffCoeffs(doublereal* const dt)
{
// Method for MultiTransport class:
// solveLMatrixEquation();
// const doublereal c = 1.6/GasConstant;
// for (size_t k = 0; k < m_nsp; k++) {
// dt[k] = c * m_mw[k] * m_molefracs[k] * m_a[k];
// }
throw CanteraError("HighPressureGasTransport::getThermalDiffCoeffs",
"Not yet implemented.");
}
void HighPressureGasTransport::getBinaryDiffCoeffs(const size_t ld, doublereal* const d)
{
vector_fp PcP(5);
size_t nsp = m_thermo->nSpecies();
vector_fp molefracs(nsp);
m_thermo->getMoleFractions(&molefracs[0]);
update_T();
// Evaluate the binary diffusion coefficients from the polynomial fits.
// This should perhaps be preceded by a check to see whether any of T, P, or
// C have changed.
//if (!m_bindiff_ok) {
updateDiff_T();
//}
if (ld < nsp) {
throw CanteraError("HighPressureTransport::getBinaryDiffCoeffs()", "ld is too small");
}
doublereal rp = 1.0/m_thermo->pressure();
for (size_t i = 0; i < nsp; i++) {
for (size_t j = 0; j < nsp; j++) {
// Add an offset to avoid a condition where x_i and x_j both equal
// zero (this would lead to Pr_ij = Inf):
doublereal x_i = std::max(Tiny, molefracs[i]);
doublereal x_j = std::max(Tiny, molefracs[j]);
// Weight mole fractions of i and j so that X_i + X_j = 1.0:
x_i = x_i/(x_i + x_j);
x_j = x_j/(x_i + x_j);
//Calculate Tr and Pr based on mole-fraction-weighted crit constants:
double Tr_ij = m_temp/(x_i*Tcrit_i(i) + x_j*Tcrit_i(j));
double Pr_ij = m_thermo->pressure()/(x_i*Pcrit_i(i) + x_j*Pcrit_i(j));
double P_corr_ij;
if (Pr_ij < 0.1) {
// If pressure is low enough, no correction is needed:
P_corr_ij = 1;
}else {
// Otherwise, calculate the parameters for Takahashi correlation
// by interpolating on Pr_ij:
P_corr_ij = setPcorr(Pr_ij, Tr_ij);
// If the reduced temperature is too low, the correction factor
// P_corr_ij will be < 0:
if (P_corr_ij<0) {
P_corr_ij = Tiny;
}
}
// Multiply the standard low-pressure binary diffusion coefficient
// (m_bdiff) by the Takahashi correction factor P_corr_ij:
d[ld*j + i] = P_corr_ij*rp * m_bdiff(i,j);
}
}
}
void HighPressureGasTransport::getMultiDiffCoeffs(const size_t ld, doublereal* const d)
{
// Not currently implemented. m_Lmatrix inversion returns NaN. Needs to be
// fixed. --SCD - 2-28-2014
throw CanteraError("HighPressureTransport:getMultiDiffCoeffs()",
"Routine not yet implemented");
// Calculate the multi-component Stefan-Maxwell diffusion coefficients,
// based on the Takahashi-correlation-corrected binary diffusion coefficients.
// update the mole fractions
update_C();
// update the binary diffusion coefficients
update_T();
updateThermal_T();
// Correct the binary diffusion coefficients for high-pressure effects; this
// is basically the same routine used in 'getBinaryDiffCoeffs,' above:
size_t nsp = m_thermo->nSpecies();
vector_fp molefracs(nsp);
m_thermo->getMoleFractions(&molefracs[0]);
update_T();
// Evaluate the binary diffusion coefficients from the polynomial fits -
// this should perhaps be preceded by a check for changes in T, P, or C.
updateDiff_T();
if (ld < m_nsp) {
throw CanteraError("HighPressureTransport::getMultiDiffCoeffs()",
"ld is too small");
}
for (size_t i = 0; i < m_nsp; i++) {
for (size_t j = 0; j < m_nsp; j++) {
// Add an offset to avoid a condition where x_i and x_j both equal
// zero (this would lead to Pr_ij = Inf):
doublereal x_i = std::max(Tiny, molefracs[i]);
doublereal x_j = std::max(Tiny, molefracs[j]);
x_i = x_i/(x_i+x_j);
x_j = x_j/(x_i+x_j);
double Tr_ij = m_temp/(x_i*Tcrit_i(i) + x_j*Tcrit_i(j));
double Pr_ij = m_thermo->pressure()/(x_i*Pcrit_i(i) + x_j*Pcrit_i(j));
double P_corr_ij;
if (Pr_ij < 0.1) {
P_corr_ij = 1;
}else {
P_corr_ij = setPcorr(Pr_ij, Tr_ij);
if (P_corr_ij<0) {
P_corr_ij = Tiny;
}
}
m_bdiff(i,j) *= P_corr_ij;
}
}
m_bindiff_ok = false; // m_bdiff is overwritten by the above routine.
// Having corrected m_bdiff for pressure and concentration effects, the
// routine now proceeds the same as in the low-pressure case:
// evaluate L0000 if the temperature or concentrations have
// changed since it was last evaluated.
if (!m_l0000_ok) {
eval_L0000(molefracs.data());
}
// invert L00,00
int ierr = invert(m_Lmatrix, m_nsp);
if (ierr != 0) {
throw CanteraError("HighPressureGasTransport::getMultiDiffCoeffs",
"invert returned ierr = {}", ierr);
}
m_l0000_ok = false; // matrix is overwritten by inverse
m_lmatrix_soln_ok = false;
doublereal prefactor = 16.0 * m_temp
*m_thermo->meanMolecularWeight()/(25.0*m_thermo->pressure());
for (size_t i = 0; i < m_nsp; i++) {
for (size_t j = 0; j < m_nsp; j++) {
double c = prefactor/m_mw[j];
d[ld*j + i] = c*molefracs[i]*(m_Lmatrix(i,j) - m_Lmatrix(i,i));
}
}
}
doublereal HighPressureGasTransport::viscosity()
{
// Calculate the high-pressure mixture viscosity, based on the Lucas method.
double Tc_mix = 0.;
double Pc_mix_n = 0.;
double Pc_mix_d = 0.;
double MW_mix = m_thermo->meanMolecularWeight();
double MW_H = m_mw[0];
double MW_L = m_mw[0];
doublereal FP_mix_o = 0;
doublereal FQ_mix_o = 0;
doublereal tKelvin = m_thermo->temperature();
double Pvp_mix = m_thermo->satPressure(tKelvin);
size_t nsp = m_thermo->nSpecies();
vector_fp molefracs(nsp);
m_thermo->getMoleFractions(&molefracs[0]);
double x_H = molefracs[0];
for (size_t i = 0; i < m_nsp; i++) {
// Calculate pure-species critical constants and add their contribution
// to the mole-fraction-weighted mixture averages:
double Tc = Tcrit_i(i);
double Tr = tKelvin/Tc;
double Zc = Zcrit_i(i);
Tc_mix += Tc*molefracs[i];
Pc_mix_n += molefracs[i]*Zc; //numerator
Pc_mix_d += molefracs[i]*Vcrit_i(i); //denominator
// Need to calculate ratio of heaviest to lightest species:
if (m_mw[i] > MW_H) {
MW_H = m_mw[i];
x_H = molefracs[i];
} else if (m_mw[i] < MW_L) {
MW_L = m_mw[i]; }
// Calculate reduced dipole moment for polar correction term:
doublereal mu_ri = 52.46*100000*m_dipole(i,i)*m_dipole(i,i)
*Pcrit_i(i)/(Tc*Tc);
if (mu_ri < 0.022) {
FP_mix_o += molefracs[i];
} else if (mu_ri < 0.075) {
FP_mix_o += molefracs[i]*(1. + 30.55*pow(0.292 - Zc, 1.72));
} else { FP_mix_o += molefracs[i]*(1. + 30.55*pow(0.292 - Zc, 1.72)
*fabs(0.96 + 0.1*(Tr - 0.7)));
}
// Calculate contribution to quantum correction term.
// SCD Note: This assumes the species of interest (He, H2, and D2) have
// been named in this specific way. They are perhaps the most obvious
// names, but it would of course be preferred to have a more general
// approach, here.
std::vector<std::string> spnames = m_thermo->speciesNames();
if (spnames[i] == "He") {
FQ_mix_o += molefracs[i]*FQ_i(1.38,Tr,m_mw[i]);
} else if (spnames[i] == "H2") {
FQ_mix_o += molefracs[i]*(FQ_i(0.76,Tr,m_mw[i]));
} else if (spnames[i] == "D2") {
FQ_mix_o += molefracs[i]*(FQ_i(0.52,Tr,m_mw[i]));
} else {
FQ_mix_o += molefracs[i];
}
}
double Tr_mix = tKelvin/Tc_mix;
double Pc_mix = GasConstant*Tc_mix*Pc_mix_n/Pc_mix_d;
double Pr_mix = m_thermo->pressure()/Pc_mix;
double ratio = MW_H/MW_L;
double ksi = pow(GasConstant*Tc_mix*3.6277*pow(10.0,53.0)/(pow(MW_mix,3)
*pow(Pc_mix,4)),1.0/6.0);
if (ratio > 9 && x_H > 0.05 && x_H < 0.7) {
FQ_mix_o *= 1 - 0.01*pow(ratio,0.87);
}
// Calculate Z1m
double Z1m = (0.807*pow(Tr_mix,0.618) - 0.357*exp(-0.449*Tr_mix)
+ 0.340*exp(-4.058*Tr_mix)+0.018)*FP_mix_o*FQ_mix_o;
// Calculate Z2m:
double Z2m;
if (Tr_mix <= 1.0) {
if (Pr_mix < Pvp_mix/Pc_mix) {
doublereal alpha = 3.262 + 14.98*pow(Pr_mix,5.508);
doublereal beta = 1.390 + 5.746*Pr_mix;
Z2m = 0.600 + 0.760*pow(Pr_mix,alpha) + (0.6990*pow(Pr_mix,beta) -
0.60)*(1- Tr_mix);
} else {
throw CanteraError("HighPressureGasTransport::viscosity",
"State is outside the limits of the Lucas model, Tr <= 1");
}
} else if ((Tr_mix > 1.0) && (Tr_mix < 40.0)) {
if ((Pr_mix > 0.0) && (Pr_mix <= 100.0)) {
doublereal a_fac = 0.001245*exp(5.1726*pow(Tr_mix,-0.3286))/Tr_mix;
doublereal b_fac = a_fac*(1.6553*Tr_mix - 1.2723);
doublereal c_fac = 0.4489*exp(3.0578*pow(Tr_mix,-37.7332))/Tr_mix;
doublereal d_fac = 1.7368*exp(2.2310*pow(Tr_mix,-7.6351))/Tr_mix;
doublereal f_fac = 0.9425*exp(-0.1853*pow(Tr_mix,0.4489));
Z2m = Z1m*(1 + a_fac*pow(Pr_mix,1.3088)/(b_fac*pow(Pr_mix,f_fac)
+ pow(1+c_fac*pow(Pr_mix,d_fac),-1)));
} else {
throw CanteraError("HighPressureGasTransport::viscosity",
"State is outside the limits of the Lucas model, 1.0 < Tr < 40");
}
} else {
throw CanteraError("HighPressureGasTransport::viscosity",
"State is outside the limits of the Lucas model, Tr > 40");
}
// Calculate Y:
doublereal Y = Z2m/Z1m;
// Return the viscosity:
return Z2m*(1 + (FP_mix_o - 1)*pow(Y,-3))*(1 + (FQ_mix_o - 1)
*(1/Y - 0.007*pow(log(Y),4)))/(ksi*FP_mix_o*FQ_mix_o);
}
// Pure species critical properties - Tc, Pc, Vc, Zc:
doublereal HighPressureGasTransport::Tcrit_i(size_t i)
{
// Store current molefracs and set temp molefrac of species i to 1.0:
vector_fp molefracs = store(i, m_thermo->nSpecies());
double tc = m_thermo->critTemperature();
// Restore actual molefracs:
m_thermo->setMoleFractions(&molefracs[0]);
return tc;
}
doublereal HighPressureGasTransport::Pcrit_i(size_t i)
{
// Store current molefracs and set temp molefrac of species i to 1.0:
vector_fp molefracs = store(i, m_thermo->nSpecies());
double pc = m_thermo->critPressure();
// Restore actual molefracs:
m_thermo->setMoleFractions(&molefracs[0]);
return pc;
}
doublereal HighPressureGasTransport::Vcrit_i(size_t i)
{
// Store current molefracs and set temp molefrac of species i to 1.0:
vector_fp molefracs = store(i, m_thermo->nSpecies());
double vc = m_thermo->critVolume();
// Restore actual molefracs:
m_thermo->setMoleFractions(&molefracs[0]);
return vc;
}
doublereal HighPressureGasTransport::Zcrit_i(size_t i)
{
// Store current molefracs and set temp molefrac of species i to 1.0:
vector_fp molefracs = store(i, m_thermo->nSpecies());
double zc = m_thermo->critCompressibility();
// Restore actual molefracs:
m_thermo->setMoleFractions(&molefracs[0]);
return zc;
}
vector_fp HighPressureGasTransport::store(size_t i, size_t nsp)
{
vector_fp molefracs(nsp);
m_thermo->getMoleFractions(&molefracs[0]);
vector_fp mf_temp(nsp, 0.0);
mf_temp[i] = 1;
m_thermo->setMoleFractions(&mf_temp[0]);
return molefracs;
}
// Calculates quantum correction term for a species based on Tr and MW, used in
// viscosity calculation:
doublereal HighPressureGasTransport::FQ_i(doublereal Q, doublereal Tr, doublereal MW)
{
return 1.22*pow(Q,0.15)*(1 + 0.00385*pow(pow(Tr - 12.,2.),1./MW)
*fabs(Tr-12)/(Tr-12));
}
// Set value of parameter values for Takahashi correlation, by interpolating
// table of constants vs. Pr:
doublereal HighPressureGasTransport::setPcorr(doublereal Pr, doublereal Tr)
{
const static double Pr_lookup[17] = {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0,
1.2, 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 4.0, 5.0};
const static double DP_Rt_lookup[17] = {1.01, 1.01, 1.01, 1.01, 1.01, 1.01,
1.01, 1.02, 1.02, 1.02, 1.02, 1.03, 1.03, 1.04, 1.05, 1.06, 1.07};
const static double A_ij_lookup[17] = {0.038042, 0.067433, 0.098317,
0.137610, 0.175081, 0.216376, 0.314051, 0.385736, 0.514553, 0.599184,
0.557725, 0.593007, 0.696001, 0.790770, 0.502100, 0.837452, 0.890390};
const static double B_ij_lookup[17] = {1.52267, 2.16794, 2.42910, 2.77605,
2.98256, 3.11384, 3.50264, 3.07773, 3.54744, 3.61216, 3.41882, 3.18415,
3.37660, 3.27984, 3.39031, 3.23513, 3.13001};
const static double C_ij_lookup[17] = {0., 0., 0., 0., 0., 0., 0., 0.141211,
0.278407, 0.372683, 0.504894, 0.678469, 0.665702, 0., 0.602907, 0., 0.};
const static double E_ij_lookup[17] = {1., 1., 1., 1., 1., 1., 1., 13.45454,
14., 10.00900, 8.57519, 10.37483, 11.21674, 1., 6.19043, 1., 1.};
// Interpolate Pr vs. those used in Takahashi table:
int Pr_i = 0;
double frac = 0.;
if (Pr < 0.1) {
frac = (Pr - Pr_lookup[0])/(Pr_lookup[1] - Pr_lookup[0]);
} else {
for (int j = 1; j < 17; j++) {
if (Pr_lookup[j] > Pr) {
frac = (Pr - Pr_lookup[j-1])/(Pr_lookup[j] - Pr_lookup[j-1]);
break;
}
Pr_i++;
}
}
// If Pr is greater than the greatest value used by Takahashi (5.0), use the
// final table value. Should eventually add in an extrapolation:
if (Pr_i == 17) {
frac = 1.0;
}
doublereal P_corr_1 = DP_Rt_lookup[Pr_i]*(1.0 - A_ij_lookup[Pr_i]
*pow(Tr,-B_ij_lookup[Pr_i]))*(1-C_ij_lookup[Pr_i]
*pow(Tr,-E_ij_lookup[Pr_i]));
doublereal P_corr_2 = DP_Rt_lookup[Pr_i+1]*(1.0 - A_ij_lookup[Pr_i+1]
*pow(Tr,-B_ij_lookup[Pr_i+1]))*(1-C_ij_lookup[Pr_i+1]
*pow(Tr,-E_ij_lookup[Pr_i+1]));
return P_corr_1*(1.0-frac) + P_corr_2*frac;
}
}
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